Reasoning about Numbers

Number Line Movements

Initially this is a virtual version of walking forwards and backwards on a number line, in order to emphasise arithmetic as the study of actions of numbers on numbers.With the addition of T (for turn around) learners can begin to reason about the actions without recourse to doing it physically, and eventually, without enacting it virtually.

Set Ratios

Given a number of counters, in how many different ways can you place them in the three regions formed from two overlapping Circles (sets A and B) so that there are the same number of counters in both A and B?

Screen shot

Screen shot

Covered-Up Sums

A selection of cells from a grid have been selected (think of the other cells as having been covered-up). Their sum is shown.Make another selection, one cell from each row and columns. What is their sum?What is going on?

​What happens if you cover-up all but two cells in each row and column?

The applet supports constructing your own grid with a specified sum.

What matters is the reasoning as to why, and why the construction works!

Reasoning About the Number LineUsing ​to the left of, to the right of, greater than and less, and also closer to ... than to ... to work out a number on the number line. One deals with whole numbers; one deals with fractions, and one deals with decimals. One uses clues of the form "the number is ... much more than an integer multiple of ..." where the divisors can be chosen to have denominators from 1 to 10.